Regular Expressions with Numerical Constraints and Automata with Counters

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Peer reviewed

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Abstract

Regular expressions with numerical constraints are an extension of regular expressions, allowing to bound numerically the number
of times that a subexpression should be matched. Expressions in this
extension describe the same languages as the usual regular expressions,
but are exponentially more succinct.
We de ne a class of nite automata with counters and a deterministic
subclass of these. Deterministic nite automata with counters can rec-
ognize words in linear time. Furthermore, we describe a subclass of the
regular expressions with numerical constraints, a polynomial-time test
for this subclass, and a polynomial-time construction of deterministic
nite automata with counters from expressions in the subclass.

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Proceedings from the 6th International Colloquium Kuala Lumpur, Malaysia, August 16-20, 2009